Magic angle and plasmon mode engineering in twisted trilayer graphene with pressure

Zewen Wu, Xueheng Kuang, Zhen Zhan, and Shengjun Yuan

Phys. Rev. B 104, 205104 – Published 5 November 2021

Abstract

Recent experimental and theoretical investigations demonstrate that twisted trilayer graphene (tTLG) is a highly tunable platform to study the correlated insulating states, ferromagnetism, and superconducting properties. Here we explore the possibility of tuning electronic correlations of the tTLG via a vertical pressure. A full tight-binding model is used to accurately describe the pressure-dependent interlayer interactions. Our results show that pressure can push a relatively larger twist angle (for instance, $1 . 89^{\circ}$ ) tTLG to reach the flat-band regime. Next, we obtain the relationship between the pressure-induced magic angle value and the critical pressure. These critical pressure values are almost half of that needed in the case of twisted bilayer graphene. Then, plasmonic properties are further investigated in the flat-band tTLG with both zero-pressure magic angle and pressure-induced magic angle. Two plasmonic modes are detected in these two kinds of flat-band samples. By comparison, one is a high energy damping-free plasmon mode that shows similar behavior, and the other is a low energy plasmon mode (flat-band plasmon) that shows obvious differences. The flat-band plasmon is contributed by both interband and intraband transitions of flat bands, and its divergence is due to the various shape of the flat bands in tTLG with zero-pressure and pressure-induced magic angles. This may provide an efficient way of tuning between regimes with strong and weak electronic interactions in one sample and overcoming the technical requirement of precise control of the twist angle in the study of correlated physics.

Received 5 August 2021
Revised 12 October 2021
Accepted 27 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.205104

Physics Subject Headings (PhySH)

Electronic structure Plasmonics

Graphene

Tight-binding model

Condensed Matter, Materials & Applied PhysicsPlasma Physics

Authors & Affiliations

Zewen Wu ^1,2, Xueheng Kuang^1,3, Zhen Zhan^1,*, and Shengjun Yuan ^1,2,†

¹Key Laboratory of Artificial Micro- and Nano-structures of the Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
²Institute for Molecules and Materials, Radboud University, Heijendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands
³Imdea Nanoscience, Faraday 9, 28015 Madrid, Spain

^*Corresponding author: zhen.zhan@whu.edu.cn
^†Corresponding author: s.yuan@whu.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 104, Iss. 20 — 15 November 2021

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) The upper panel shows the top view of the atomic configuration of $tTLG − A \tilde{A} A − 6 . 01^{\circ}$ . High-symmetry stacking regions of AAA, ABA, BAB are marked by black, red, and blue circles, respectively. The lower panel shows a schematic representation of these high-symmetry stacking patterns. The number 6.01 stands for the twist angle $θ = 6 . 01^{\circ}$ . (b) The out-of-plane displacement of relaxed $tTLG − A \tilde{A} A − 1 . 35^{\circ}$ without pressure, relaxed $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ without and with 4 GPa vertical pressure, respectively. (c) Band structure and density of states of relaxed $tTLG − A \tilde{A} A − 1 . 35^{\circ}$ under ambient pressure. (d) and (e) Band structure and density of states of relaxed $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ without and with 4 GPa vertical pressure, respectively.
Reuse & Permissions
Figure 2
(a) The band width and band gap of $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ versus the vertical pressure for the rigid and relaxed cases, respectively. The red and blue triangular symbols stand for the band width and band gap in the relaxed case, respectively. The red and blue star symbols stand for the band width and band gap in the rigid case, respectively. (b) Pressure-induced magic angle as a function of the critical compression. The blue dashed line is for the tTLG case and the red dashed line is for the tBG case that is extracted from Ref. [15].
Reuse & Permissions
Figure 3
The electronic properties of relaxed $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ under ambient and high pressures. (a) and (c) The layer-projected weights of band eigenstates of $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ under ambient and 4 GPa vertical pressures, respectively. The thickness of the lines represent the weight of band eigenstates. (b) and (d) The band structure and inverse participation ratio (IPR) of the $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ under ambient and 4 GPa external pressure, respectively. (e) and (f) Calculated local density of states (LDOS) mappings of van Hove singularities near the Fermi level of $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ without pressure and with 4 GPa pressure.
Reuse & Permissions
Figure 4
Plasmonic properties of relaxed $tTLG − A \tilde{A} A$ . The figure is organized in columns. In each column, the upper panel shows the loss function ( $- Im (1 / ɛ)$ ) and the lower panel shows the imaginary part of the frequency-dependent dynamic polarization function $- Im (Π (q, ω))$ . (a) Result for $tTLG − A \tilde{A} A − 1 . 35^{\circ}$ under ambient pressure. (b) and (c) Results for $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ under vertical pressure of 4 GPa and under ambient pressure, respectively. The wave vectors are along $Γ$ to M in the first Brillouin zone. The temperature is 1 K and chemical potential is $μ = 0$ .
Reuse & Permissions
Figure 5
(a) The real part of the frequency-dependent dielectric function of the relaxed $tTLG − A \tilde{A} A − 1 . 35^{\circ}$ under ambient pressure. (b) and (c) The real part of the frequency-dependent dielectric function of relaxed $tTLG − A \tilde{A} A − 1 . 89^{\circ}$ under 4 GPa and ambient vertical pressures, respectively. The red dashed line indicates the zero of the real part of the dielectric function.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics